It is proposed to investigate methods for the design of sequential clinical trials to determine which of two treatments is best. Particular attention will be given to determining allocation rules which allow the experimenter to draw reliable conclusions while submitting a minimum number of patients to the inferior treatments. Concomitant variables will be introduced to reduce the effect of variability among patients in such factors as initial severity of the disease. Longitudinal studies in which there is a time lag between the initiation of treatment and response will be considered. Especially in these cases the problems of competing risks will be studied. Problems of selecting a subset containing the "best" population from a large group of populations will also be considered.